Information on Result #682599

Linear OA(5126, 15655, F5, 25) (dual of [15655, 15529, 26]-code), using construction X applied to C([0,12]) ⊂ C([0,10]) based on
  1. linear OA(5121, 15626, F5, 25) (dual of [15626, 15505, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
  2. linear OA(597, 15626, F5, 21) (dual of [15626, 15529, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
  3. linear OA(55, 29, F5, 3) (dual of [29, 24, 4]-code or 29-cap in PG(4,5)), using

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(5127, 15656, F5, 25) (dual of [15656, 15529, 26]-code) [i]Code Embedding in Larger Space
2Linear OA(5128, 15657, F5, 25) (dual of [15657, 15529, 26]-code) [i]
3Linear OOA(5126, 14814, F5, 2, 25) (dual of [(14814, 2), 29502, 26]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
4Linear OOA(5126, 14814, F5, 3, 25) (dual of [(14814, 3), 44316, 26]-NRT-code) [i]
5Digital (101, 126, 14814)-net over F5 [i]
6Linear OA(5127, 15657, F5, 25) (dual of [15657, 15530, 26]-code) [i]Construction X with VarÅ¡amov Bound
7Linear OA(5128, 15659, F5, 25) (dual of [15659, 15531, 26]-code) [i]
8Linear OA(5129, 15661, F5, 25) (dual of [15661, 15532, 26]-code) [i]
9Linear OOA(5126, 7827, F5, 2, 25) (dual of [(7827, 2), 15528, 26]-NRT-code) [i]OOA Folding
10Linear OOA(5126, 5218, F5, 3, 25) (dual of [(5218, 3), 15528, 26]-NRT-code) [i]